Question

A 68 kg hiker walks at 5.0 km/h up a 9% slope. The indicated incline is the ratio of the vertical distance and the horizontal distance expressed as percentage.
What is the necessary metabolic power?

Hint: You can model her power needs as the sum of the 380 W power to walk on level ground plus the power needed to raise her body by the appropriate amount. Assume that the efficiency of the body in using energy is 25%.

Answer 1

The power is calculated using the formula:

Power = Work / Time

where Work = Force * Distance , therefore:

Power = Force * Distance / Time

Power = Force * Velocity


Converting the velocity in units of m/s:

Velocity = (5km / h) (1000m / km) (1h / 3600s)
Velocity = 1.39 m/s 

The force is equal to the y-component of the hikers weight:

Force = Wy * g = W * sin θ * g

 

Let us first find the angle θ. By definition the slope is equivalent to:

slope = tan θ = ratio of vertical and horizontal distance

tan θ = 0.09

θ = 5.14˚

Therefore, Force = 68 kg * sin(5.14˚) * 9.8 m/s^2
Force = 666.4 * sin (5.14) = 59.73 N 

Calculating for power:
Power = 59.73 N * 1.39 m/s = 82.96 W
Since the hikers efficiency is 25%, to determine the metabolic power: 
Metabolic Power = 82.96 W / 0.25 = 331.83 watts